On limitations of the Bruggeman formalism for inverse homogenization

The Bruggeman formalism provides an estimate ${\text{eps}}_{hcm}^{Br}$ of the relative permittivity of a homogenized composite material (HCM), arising from two component materials with relative permittivities ${\text{eps}}_a$ and ${\text{eps}}_b$. It can be inverted to provide an estimate of ${\text{eps}}_a$, from a knowledge of ${\text{eps}}_{hcm}^{Br}$ and ${\text{eps}}_b$. Numerical studies show that the inverse Bruggeman estimate ${\text{eps}}_a$ can be physically implausible when (i) $Re\{{\text{eps}}_{hcm}^{Br}\}\mathrm{/}Re\{{\text{eps}}_b\}>0$ and the degree of HCM dissipation is moderate or greater; or (ii) $Re\{{\text{eps}}_{hcm}^{Br}\}\mathrm{/}Re\{{\text{eps}}_b\}<0$ regardless of the degree of HCM dissipation. Furthermore, even when the inverse Bruggeman estimate is not obviously implausible, huge discrepancies can exist between this estimate and the corresponding estimate provided by the inverse Maxwell Garnett formalism.